Precision T5500 won't boot

Precision T5500 dual-Xeon workstation previously working fine, suddenly won't boot when front panel power switch is pressed. No light (green or amber) appears in the power switch and no other front panel LEDs appear lit. Nothing appears on the monitor screen.

I start with the power cable unplugged and only the monitor cable attached. When I plug in the cable, the front panel lights flash momentarily and fans turn briefly. If I then press and hold the test button on the power supply, the adjacent LED lights up steady green and stays lit. The power supply, system, second CPU riser, and video card fans spin, the optical disk LED lights momentarily, and the front panel hard disk LED lights steadily but no other front panel LEDs light and the system doesn't boot. I do notice that an amber LED on the lower-right corner of the motherboard lights and remains lit even for some time after mains power is removed (while capacitors drain, I suppose).

What's the most likely cause? What are my chances of being able to repair it?